Combination of Fractional-Order, Adaptive Second Order and Non-Singular Terminal Sliding Mode Controls for Dynamical Systems with Uncertainty and Under-Actuation Property

This paper introduces a new type of control strategy for dynamical systems subjected to uncertainties. The suggested controller combines the capabilities of sliding mode control with fractional-order control and a specified adaption law. The stability of the closed-loop system is examined based on Lyapunov stability theory. This control scheme can be employed in many conventional systems; however, in this paper, we try to apply it to an under-actuated system as a novel extension to the variety of its applications. The idea originates from the practical features of fractional calculus including the facts that the fractional derivative has a memory of past values and it preserves a large stability region and has more free parameters to enhance the performance of the controller. Computer simulations are included to highlight the efficiency and applicability of the proposed controller in control of an under-actuated system even in the presence of parameter uncertainties.